1. Field of the Invention
The present invention relates generally to impedance matching in radio frequency circuits, and more particularly relates to active impedance matching of electrically small antennas to achieve broadband impedance matching.
2. Description of the Prior Art
In a radio frequency circuit, the impedance of a source or load is characterized by a resistive component and a reactive component. The two components can be viewed as orthogonal vectors with the resultant impedance being the sum of these two vectors. Methods of complex algebra are commonly used to describe electrical impedances with the real part of an impedance representing its resistive component and the imaginary part of the impedance representing its reactive component. As the frequency of operation changes for a typical broadband circuit, the value of the resistive component remains substantially constant while the value of the reactive component changes.
To achieve maximum power transfer in a radio frequency circuit, a circuit receiving a signal (load) should have an impedance with its resistance equal to the resistance of the impedance of the circuit generating the signal (source) and a reactance that is equal in magnitude but of opposite sign to the reactance of the circuit generating the signal. When the load and source are of different impedances, it is desirable to interpose an impedance matching circuit between the source and the load to transform the source and load impedances to a common value, usually the characteristic impedance (which is a real, and not complex, quantity) of the transmission line connecting the source and the transformed load. When the source and the load are properly matched to the characteristic impedance, maximum power transfer is achieved and signal reflections are minimized.
In the arithmetic of complex variables, the condition for maximum power transfer is obtained when the circuit receiving a signal has an impedance (or admittance) which is the complex conjugate of the impedance (or admittance) of the circuit generating the signal.
For passive circuits, the reactive component is capacitive, inductive or a combination of these parameters. For a capacitive reactance, the reactance of the circuit varies according to the equation: ##EQU1## where F is the frequency of operation and C is the capacitance value of the circuit. The frequency dependent nature of the capacitive reactance can readily be appreciated by use of a graphical impedance chart, such as a Smith chart illustrated in FIG. 1. Referring to FIG. 1, the capacitive reactance is infinite at direct current (DC) 2 and becomes progressively smaller with increasing frequency. This is represented as a clockwise rotation about the outside circle of the chart, toward the lower half (negative reactance) region of the chart.
Similarly, for inductive circuits, the reactance varies according to the equation: EQU X.sub.1 =2.multidot..pi..multidot.F.multidot.L
where F is the frequency of operation and L is the inductance value of the circuit. Again referring to FIG. 1, the inductive reactance at DC 4 is zero ohms and progressively increases into the upper portion (positive reactance) of the chart with increasing frequency. This frequency dependence is seen as a clockwise rotation about the chart from the zero .OMEGA. point 4. The behavior of such conventional passive, bilateral reactive components complies with Foster's reactance theorem which states that the impedance of any passive circuit is characterized by a reactance that exhibits a positive slope with frequency at all frequencies. As such, these components can be said to exhibit Foster impedances, and, since their resistance values are very small, they can be said to exhibit Foster reactances, that is, a Foster impedance having a negligible resistance.
In a typical impedance matching circuit, it is a common objective to neutralize the reactive components of a load such that only a resistive component remains. From FIG. 1, it can be seen that capacitive reactance is negative (current lagging) while inductive reactance is positive (current leading). In the simplest case, without regard to impedance transformation, the cancellation of a load with capacitive reactance requires an inductive reactance of equal magnitude. In a similar fashion, for inductive loads, a capacitive reactance of equal magnitude is required to cancel the inductive reactive component.
However, as is illustrated in FIG. 1, the magnitudes of both the inductive and capacitive reactance vary with frequency. Further, the magnitudes of the reactance vary in opposite directions. Therefore, using conventional capacitive and inductive components, the total reactance can be eliminated at only a single frequency known as the resonant frequency of the circuit.
In order to overcome the problem of single frequency reactance cancellation, active circuits have been employed to create "negative capacitance" and "negative inductance" values. These active circuits attempt to create reactances which mirror those of the corresponding positive capacitance and inductance, respectively. Such reactance characteristics violate Foster's reactance theorem and, therefore, can be generally referred to as non-Foster reactances. Referring to the Smith chart of FIG. 2, a curve 6 of capacitive reactance for a conventional capacitor is illustrated between a first frequency, F1, and a second frequency, F2. This curve follows the characteristics described in FIG. 1 for a capacitive reactance. FIG. 2 further illustrates a theoretical curve 8 between F1 and F2 for a negative capacitor of equal magnitude to the positive capacitor.
The curve 8 for the negative capacitor begins with a high positive reactance which becomes smaller with frequency (counter clockwise rotation). At all frequencies, this capacitive reactance is exactly equal and opposite to that of the conventional capacitor curve 6. Therefore, for a circuit which combines these two elements, reactive cancellation will occur at all frequencies, rather than just one.
Various circuit topologies have been experimented with in an effort to achieve both negative capacitors and negative inductors which exhibit low loss, non-Foster impedance properties at radio frequencies. Several topologies for negative inductors are illustrated in the article "The Design of Active Floating Positive and Negative Inductors in MMIC Technology", S. El Khoury, IEEE Microwave and Guided Wave Letters, Vol. 5, No. 10, October 1995. Exemplary topologies for realizing active negative capacitors are disclosed in the article "An NIC-Based Negative capacitance circuit for Microwave Active Filters," Sussman-Fort et al., International Journal of Microwave and Millimeter-Wave Computer Aided Engineering, Vol. 5, No. 4, 271-277 (1995). Each of these articles is incorporated herein by reference.
FIG. 3 is a simplified schematic diagram of a negative inductor circuit disclosed in the Khoury article. The circuit includes an input field effect transistor (FET) 10, an output FET 12, a coupling FET 14 and a capacitor 16. The FET's 10,12,14 are conventional devices each having a gate terminal, a source terminal and a drain terminal. The gate terminal of the input FET 10 functions as the input terminal of the negative inductor circuit. The gate terminal of the input FET 10 also receives a feedback signal from the drain terminal of the output FET 12. The input FET 10 generates a differential signal between the source terminal and drain terminal. The coupling FET 14 is interposed between the input FET 10 and output FET 12 to provide additional gain and isolation. The source terminal of the coupling FET 14 is connected to the drain terminal of the input FET 10. The drain terminal of the coupling FET 14 is connected to the gate terminal of the output FET 12. The gate terminal of the coupling FET 14 is connected to the source terminal of both the input FET 10 and output FET 12. The capacitor 16 is coupled across the drain and gate of the output FET 12. The output FET 12, which is configured as an inverting transconductance device, transforms the capacitance from gate to source into a negative inductance.
FIG. 4 illustrates an exemplary circuit topology of a negative capacitor circuit disclosed in the Sussman-Fort et al. article. The circuit illustrated employs two FET's 18,20 to transform a capacitance from a capacitor 22 into a negative capacitance. The circuit is described as a two port negative impedance converter. The first port is an input port and is taken at the source terminal of the first FET 18. The second port is connected to the drain of the first FET 18. The capacitor 22 is connected between the second port and circuit ground. The gate terminal of the first FET 18 is connected to the drain terminal of the second FET 20. This junction has a return path to circuit ground through a first resistor 24. The gate terminal of the second FET 20 is connected to the drain terminal of the first FET 18. The source terminal of the second FET 20 has a return path to circuit ground through a second resistor 26. The parameters of the components in this circuit are determined using computer aided design techniques which are described in detail in the Sussman-Fort et al. article.
A commonly encountered component in a radio frequency circuit is an antenna. Antennas typically present complex load impedances which vary significantly with frequency. FIG. 5 illustrates a simplified diagram of a signal source 30 driving an antenna 32. Interposed between the source 30 and antenna 32 is an impedance matching circuit 34. Conventional narrow band impedance matching circuits 34 are designed to transform the impedance presented by the antenna 32 to the complex conjugate of the impedance of the source 30 at a specific frequency or approximately over a small band of frequencies.
The complicated antenna impedance is affected by a number of characteristics including the electrical length of the antenna. The electrical length of an antenna is expressed in wavelengths of the operating frequency of the antenna. When an antenna is fabricated with an electrical length significantly less than one-half wavelength, it is commonly referred to as an electrically small antenna.
In general, the impedance of an electrically small antenna may be modeled by a simple parallel resonant circuit (small loop antennas) or by a simple series resonant circuit (small dipole antennas). The smaller the antenna the more faithfully the simple resonant circuit models replicate actual antenna behavior with respect to their inductance and capacitance and radiation resistance. However, it should be kept in mind that when the antenna is so small that its radiation resistance is comparable to the loss resistance associated with the antenna, then the loss resistance must be taken into account in the model.
FIG. 6 illustrates a model of a small dipole antenna. Referring to FIG. 6, the antenna 32 is modeled as a resistor 36, a capacitor 38 and an inductor 40 all connected in series. Both the capacitor 38 and inductor 40 act similarly to conventional components and present a frequency dependent reactance as previously discussed, and illustrated in FIG. 1. However, the resistor 36 in the antenna model has two components, the radiation resistance of the antenna, R.sub.r and a loss resistance R.sub.L. For the electrically small antennas considered here, the loss resistance is usually much less than the radiation resistance, and will be treated as zero ohms for the sake of simplicity. Unlike a conventional resistor, R.sub.r is a frequency dependent variable for the antenna 32. The magnitude of the radiation resistance increases as the frequency squared. The resistance and reactance variations for an exemplary small dipole antenna are illustrated graphically in FIGS. 7A and 7B respectively.
For any given frequency of operation, the antenna 32 presents a known impedance to the impedance matching circuit 34. The impedance matching circuit 34 can be designed to cancel the net reactance of the antenna inductance 40 and capacitance 38 as well as to transform the radiation resistance 36 to match the impedance of the source 30. However, as the frequency of operation changes, the impedance of the antenna 32 also changes and the simple matching circuit 34 formed with conventional Foster reactance components no longer presents the proper impedance to the source 30. This results in an undesirable impedance mismatch between the signal source 30 and antenna 32.
An attempt to overcome the problem of broad band impedance matching of an antenna using a negative inductor circuit is described in U.S. Pat. No. 5,296,866 to Sutton. The Sutton patent is directed to low frequency antennas, especially large pick up coils well suited for detecting low frequency electromagnetic waves. The Sutton patent employs a low frequency operational amplifier circuit configured as a negative inductor to cancel the large positive inductive reactance presented by the coil. In low frequency pick up coils, the large amount of wire used presents a large resistance which does not change with frequency. The Sutton patent discloses the use of an active "negative resistance" circuit whose resistance is independent of frequency to cancel a large portion of this resistance. However, the Sutton patent does not teach or suggest means for broad band matching of an electrically small antenna.